Peter Tatchell: ‘To me, a suffering to my family, my neighbour, or a stranger in a faraway country – it’s all the same.’ Photograph: Felix Clay for the Guardian

When Downing Street hosted its annual reception for gay, lesbian, bisexual and transgender luminaries this week, the only real surprise of the night was one conspicuous absence. In a congratulatory speech to more than 150 activists, campaigners and celebrities, the prime minister paid tribute to many of the guests, and in particular thanked Peter Tatchell for his 21-year campaign for gay marriage. But Tatchell wasn't there to hear him, because he wasn't invited.

Tatchell spent the evening alone at his desk in his one-bedroom council flat, working on a campaign against homophobia in Russia. The desk and chair comprise the only discernible furniture in his front room. As I take in the scene, he murmurs nervously: "She's thinking it's a madman's home." In truth, that's what it looks like. Waist-high stacks of manila folders, ring binders, A5 posters and box files fill the room, the only visible carpet space a sliver just wide enough for him to reach his desk. The walls are more or less wallpapered with political posters and badges and radical iconography. I don't even realise there's a sofa until he nods to a mountain of paperwork along one wall, underneath which one is apparently buried. "But I haven't sat on it for about 15 years."

It's twice that long since Tatchell last attended a wedding, and he dreads the prospect of gay weddings adopting all the consumerist excess of heterosexual ceremonies. He is "not personally a great fan of marriage", and has never wanted it for himself – yet already he is hard at work on a campaign for further reforms of its laws, having identified no fewer than six inequalities in the new legislation. As he outlines his proposals he raises his voice and almost leans into an imaginary lectern, the old Tatchell zeal undimmed by any temptation to ease off and savour the moment of success.

"I intend to start recampaigning around my proposal for an entirely new legal framework of relationship recognition and rights. At the moment civil partners and spouses have legal privileges over single people. I don't see why single people should be denied the same rights, and this is increasingly important as more than a quarter of the population are single and living alone. They are discriminated against, and that is wrong."

Tatchell thinks singles should be allowed to nominate a friend or relative to be their "significant other", who would enjoy the same exemption from inheritance tax as a spouse, and the same legal rights as a next of kin. Under his proposals, heterosexual couples would also be given the right to choose between a civil partnership and a wedding. In addition, all couples would be offered a third choice: "To enter a new legal framework that's completely different and in tune with modern lifestyles and relationships." If a couple doesn't fancy the one-size-fits-all contract of a marriage or civil partnership, "they should have the option of picking and mixing from a menu of rights and responsibilities. They can decide which legal rights and responsibilities conferred by marriage they'd like to sign up to – and which they'd ditch."

Tatchell has been out of step with the prevailing mainstream consensus for almost half a century, and even within the gay rights movement he is one of very few voices still arguing for radical liberation politics. While most campaigners have rejoiced in the equality victories of the last 15 years, his ambivalence about the equality agenda has left him increasingly marginalised. He fought hard for gay marriage, but accepts that its success was the final nail in the coffin of liberation politics. "For now at least."

"Equality is an important principle, but by itself it's not enough. If we merely seek equality for LGBT people, what we're saying is that we accept the status quo, we merely want our place in it. This represents an abandonment of any critical perspective on society as it is. It is an agenda about conformism and assimilation – whereas in the days of the Gay Liberation Front the word equality never passed our lips. We wanted social transformation, to benefit LGBT people and straight people as well. We recognised that everything wasn't hunky-dory for heterosexuals – rubbish sex education in schools, many women were dissatisfied with marriage, the laws against sexually explicit imagery were repressive – so we had an agenda about changing society. We dreamed of what society could be, rather than accepting society as it was. One of our slogans was "Innovate, don't assimilate".

His legal pick and mix menu makes perfect sense to a liberation activist interested in changing society, but would probably sound pointless to most young gay people today, so I wonder what his teenage self would have made of life in 2013 for LGBT people in Britain. Would he have been thrilled by all the changes, or dismayed? He hesitates a moment before picking his words carefully. "I'm overjoyed that we've got rid of so much homophobic discrimination. That's a huge and positive achievement that has made a real and tangible difference to the lives of LGBT people. No regrets about that at all. But I still hold on to the vision of something better – a social transformation that can liberate us all."

Peter Tatchell at home in London aged 21. Photograph: Richard Saker

Mainstream opinion didn't much like the look of his vision when he first started campaigning 46 years ago. Born in Australia in 1952, he came to England at 21 to avoid the draft for Vietnam, and became active in the Gay Liberation Front. In 1983 he stood for Labour in the safe seat of Bermondsey, only to lose to Simon Hughes, after the Liberal Party fought an ugly, homophobic smear campaign against him. He says he knew perfectly well that Hughes was gay too, but the Labour party didn't want him talking about his own sexuality, and back then he didn't believe in outing. A decade later he changed his mind, and published a list of bishops and Tory MPs who condemned homosexuality in public but were secretly gay – but the outings did not endear him to public opinion. "When Tory MPs' adulterous affairs were being exposed, everyone said that's OK 'cos they're two-faced hypocrites. But when we exposed hypocrites I was denounced as a homosexual terrorist!"

So it's hardly surprising that when the Daily Mail declared him a hero, he thought it had to be a prank. When his great – if somewhat unlikely – friend, the former Cosmopolitan editorMarcelle d'Argy Smith, of Cosmopolitan, rang him up to tell him, his first thought was to check the date on his watch. But it wasn't 1 April, so he went off to his local WH Smith. Seeing the headline, at once he began scouring the ceiling for secret cameras, convinced Jeremy Beadle was about to spring out. Only after rifling through the whole pile of papers, to make sure a fake issue hadn't been planted on the top, did he accept it was real. Tatchell's dramatic 1999 citizen's arrest of Robert Mugabe in London, for crimes against the people of Zimbabwe, had transformed him overnight into a national treasure. "I had very strange mixed emotions. My main reaction was, at last they've realised what I'm about. I work for human rights, for everyone. For me, the suffering of the people in Zimbabwe is just as important as the suffering of people in Britain or anywhere else. I'm really glad the Daily Mail has finally got the message." How the Daily Mail could have been unaware of this for so long I do not know, for a quick skim over Tatchell's website is enough to grasp the limitless scope of his human rights work.

He likes issues no one else is doing much about – "I'll concentrate on what many people see as lost and hopeless causes, West Papua, the western Sahara, Somaliland" – but beyond that he has no criteria for selecting battles to fight. The more he talks, the clearer it becomes that he is genuinely incapable of switching off.

"I always see things in terms of being part of one big global family. To me, a suffering to my family, my neighbour, or a stranger in a faraway country – it's all the same." In theory, of course, we all think that, too – but in reality most people are much more moved to help a neighbour than a faraway stranger. Isn't he? "No, it depends on how much suffering is involved, and whether anybody else knows about it and cares." I ask if he realises quite how unusual that makes him. "But to me it seems normal." Hasn't he noticed that most people, including activists, develop a protective filter over time to screen out all the injustices they can't solve? "Yes," he concedes. "And it does cause me a lot of problems, because if I hear about some particularly grotesque human rights abuse, I will find it difficult sleeping at night." Literally? "Literally."

How can he live like this? If you were looking for clues to help understand Tatchell, his evangelical Christian parents would probably be the last place you'd look – but I think they might explain a lot about him. He rejected their faith wholeheartedly, but seems to have inherited the singular emotional mindset of a missionary. "They always taught me that I should follow my own conscience, and not follow the crowd or the fashion of the day. They said: be responsible for your own actions, don't do things because other people do them, think for yourself." Temperamentally, he seems much more suited to an evangelical congregation than a modern Gay Pride march.

He hates being called a martyr, and doesn't care for my alternative suggestion of "monkish" either, but his lifestyle does suggest more than a hint of hair shirt. For 45 years he lived on earnings of £7,000-£8,000, from journalism and research, and only began paying himself a salary (£29,000) from his human rights foundation last year. Donations from well-wishers just about keep the foundation afloat, but he works 14 to 16 hours a day, seven days a week, and has not had a holiday for six years. He could have bought his flat for £15,000 in 1996, under the right to buy, but declined on moral grounds. He doesn't have a shower or a washing machine, eats abstemiously and exercises religiously ("A six-pack at 61's not bad, is it?" he says as he invites me to punch his stomach. "Harder! Harder!" It feels like punching a slab of frozen steak.) His Weeping Fig tree is all but dead ("You can see why I don't have children or pets"), and his ancient record player can't have been touched in a decade, judging from the thick cocoon of dust.

If he had more money he says he'd get a bigger flat, banish paperwork from the living room, and confine his work to office hours. I don't believe him for a minute – he'd have a mansion crammed to the rafters within a week, making him work even harder – and an old Eleanor Roosevelt line comes to mind, about people who would rather curse the darkness than light a candle. Tatchell was invited to Lambeth palace recently by the Archbishop of Canterbury – an unprecedented meeting, and another signifier of how much has changed since Tatchell invaded a previous archbishop's pulpit mid-sermon back in 1998. Both encounters were thrilling in different ways – but I wonder which he found the more enjoyable, and his answer doesn't surprise. "I wouldn't say I necessarily enjoyed either. What gave me most satisfaction was going into the pulpit."

But I guess wrong when I ask if he was secretly pleased to be excluded from the Downing Street reception. It would have been his idea of hell, wouldn't it? He nods wordlessly. "Yes, but I would have preferred to be invited – and I would have gone. So I could personally thank David Cameron – and also to make the point that he said it was about equality. That means straight people should have the right to enter civil partnerships." Tatchell has learned that his name was on the original guest list, but somebody vetoed it. He doesn't know who. Can he guess why? "Maybe he thought I was going to cover him in pink glitter, or superglue myself to the cabinet table.

"They don't seem to get it. When I'm invited somewhere and there are rules, I tend to obey them. It's when they're not expecting it – that's when I strike."

• This article was amended on 29 July 2013. The original said that the "Lib Dems fought an ugly, homophobic smear campaign against him [Peter Tatchell]. This has been corrected.